Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains

TL;DR

This paper investigates the propagation of highly nonlinear solitary waves in periodic dimer granular chains through experiments, simulations, and theoretical analysis, revealing how lattice structure influences wave properties.

Contribution

It introduces a comprehensive theoretical model for heterogeneous granular chains and validates it with experiments and simulations, extending understanding of nonlinear wave dynamics in complex media.

Findings

Excellent agreement between experiments and numerical simulations.

Theoretical analysis accurately predicts wave width and speed.

Lattice structure significantly affects wave properties.

Abstract

We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer/heavier beads (stainless steel) are alternated with softer/lighter ones (PTFE beads). We find excellent agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of the dimer lattice on the properties (width and propagation speed) of the obtained highly nonlinear wave solutions.